Possibility Distribution: a unified representation for parameter estimation

Abstract-- the paper presents a possibility formulation of oneparameter estimation that unifies some usual probability formulations. Point and confidence interval estimation are unified in a single theoretical formulation and incorporated into estimators of an omnibus form: a possibility distribution. New relationships between continuous possibility distribution and probability concepts are established. The concept of specificity ordering of a possibility distribution is then used for comparing the efficiency of different estimators. The usefulness of the approach is illustrated on mean and median estimators from data sample of different size and of different probability distribution. Keywords-- efficiency, parameter estimation, possibility, probability, stochastic ordering, uncertainty.

• Type: Journal
• Year: 2009
• Where: EUSFLAT
• Authors: Gilles Mauris
• Keywords: Estimation, Estimators, EUSFLAT 2009, Fuzzy Logic, Possibility Distribution